Due to the limited spatial resolution and partial volume effects of positron emission tomography (PET), most tissue regions studied with PET are heterogeneous with respect to the physiological and/or biochemical processes being examined and with respect to the concentrations of the relevant labeled compounds in the tissue. All quantitative work up to now has made the simplifying assumption that the tissues are homogeneous, and serious misinterpretations of results obtained by use of these methods have occurred. We have studied the effects of tissue heterogeneity on determination of local cerebral glucose utilization. Mathematical models to describe the kinetics of deoxyglucose or flurordeoxyglucose uptake and metabolism in heterogeneous tissues were developed and validated in simulation, animal, and human studies. The most appropriate kinetic model and optimal experimental protocol for the measurement of cerebral glucose utilization in man with [18F]fluorodeoxyglucose and PET were identified. We are currently developing new techniques for analysis of time-series data from tracer studies in which the underlying kinetic models have not yet been established. These techniques will enable us to build appropriate kinetic models of new tracers and to extend mathematical models of currently used tracers to additional physiological and pathophysiological conditions.